The \(\alpha\)-approximation property and the weak topology in tensor products of Banach spaces (Q1373400)

Summary: We use the \(\alpha\)-approximation property for Banach spaces in order to extend particular results about the weak topology in tensor products. We also define and apply the \(\alpha\)-density property for a couple of Banach spaces \((E, F)\). We say that \((E, F)\) has the \(\alpha\)-density property if the equality between the \((E, F')\)-component of the minimal and the maximal operator ideals associated to a tensor norm \(\alpha\) holds. This property is closely related to the Radon-Nikodým property.